2019 Reasoning - Data Sufficiency

Consider two statements S1 and S2 followed by a question : S1: p and q both are prime numbers. S2: p + q is an odd integer. Question: Is pq an odd integer? Which one of the following is correct?

• S1 alone is sufficient to answer the question
• S2 alone is sufficient to answer the question
• Both S1 and S2 taken together are not sufficient to answer the question
• Both S1 and S2 are necessary to answer the question